Geodesic
Some New Bounds on Randić Energy
Kragujevac Journal of Mathematics, Tome 43 (2019) no. 3, p. 393

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Let $G=(V,E)$ be a simple graph of order $n$ with vertex set $V=V(G)=\{v_1,v_2,\ldots,v_n\}$ and edge set $E=E(G)$. Let $d_i$ be the degree of the vertex $v_i$ in $G$ for $i=1,2,\ldots, n$. The Randić matrix ${\mathbf R}={\mathbf R}(G)=||R_{ij}||_{nxn}$ is defined by $R_{ij}=eft\{\begin{array}{cl} \dfrac{1}{qrt{d_id_j}}, \mbox{if the vertices}\hspace{0.1cm} v_i\hspace{0.1cm}\mbox{and}\hspace{0.1cm} v_j\hspace{0.1cm} \mbox{are adjacent}, 0, \mbox{otherwise}. \end{array}\right.$ The eigenvalues of matrix ${\mathbf R}$, denoted by $\rho_1,\rho_2,\ldots,\rho_n$, are called the Randić eigenvalues of graph $G$. The Randić energy of graph $G$, denoted by $RE$, is defined as $RE=RE(G)=umimits_{i=1}^n|\rho_i|.$ In this paper we establish some new upper and lower bounds on Randić energy.
Classification : 05C50
Keywords: Normalized Laplacian matrix, Randić matrix, Randić energy 
@article{KJM_2019_43_3_a3,
     author = {E. Zogi\'c and B. Borovi\'canin},
     title = {Some {New} {Bounds} on {Randi\'c} {Energy}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {393 },
     publisher = {mathdoc},
     volume = {43},
     number = {3},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2019_43_3_a3/}
}
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E. Zogić; B. Borovićanin. Some New Bounds on Randić Energy. Kragujevac Journal of Mathematics, Tome 43 (2019) no. 3, p. 393 . http://geodesic.mathdoc.fr/item/KJM_2019_43_3_a3/